Econ

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Exercise 1: perfect competition

1.1 Perfect competition

The meat-processing industry in Hungary is perfectly competitive, and there are two types of firms operating, domestic and foreign. Two representative (typical) firms are the domestic-owned MM’s-grinders and the foreign-owned KK’s cutters (henceforth MM and KK), which use slightly different technology, their production functions are:

For MM: qM = L0.6 K0.4

For KK: qK = L0.5 K0.5

Currently, the wage rate is $5 and the rental rate of capital is $10.

(a) Write down the cost-minimisation condition for the two firms.

(b) What are the equations for the (long-run) expansion paths? Comment.

(d) Are foreign-owned firms (like KK) able to survive in a competitive market?

(e) Assume that KK is more efficient than MM, such that: qK =A L0.5 K0.5. A is a scaling factor, representing managerial quality (say Kostas organises production more efficiently and is better at disciplining workers). What is the value of A if both types of firms are able to stay in the market?

Everything in red is not needed, thank you.

(f) What will be the output price in this market?

(g) Assume that the demand function for processed meat is Q=225 – 9p. What is the equilibrium quantity?

(h) Calculate the elasticity of demand at the equilibrium point.

(i) If there are currently 10 domestic firms (like MM) and 5 foreign firms (like KK) in the market, how much will each of them produce?

(j) Calculate the capital and labour input for the two types of firms if qM = L0.6 K0.4 and qK =A L0.5 K0.5 (assume that A is equal to what you found in question e).

1.2 Wage Subsidies

Now the government decides to give a wage subsidy to firms for employing low-skilled workers of $1 per unit of labour input. The meat-processing industry only employs low-skilled workers, and the effective wage rate (market wage – subsidy) for both KK and MM is $4. For the moment, assume that the production functions are the same as originally (KK is not more efficient that MM):

MM: qM = L0.6 K0.4 ; KK: qK = L0.5 K0.5 4

(k) After the firms have adjusted their inputs to take into account the subsidy, what are the new expansion paths, AC and MC for the two firms? Explain.

(l) Draw in a graph the original and the after-subsidy isocost lines, production functions and expansion paths. Comment.

(m) What is the new equilibrium price and quantity?

(n) Assuming that both types of firms are able to survive, hence that KK is more efficient than MM, the production function for KK is qK =A L0.5 K0.5 (assume that A is equal to the value you found in question e), and there are still 10 domestic and 5 foreign firms in the market, how much will each firm produce in the new equilibrium?

(o) Calculate the new capital and labour input for the two types of firms if qM = L0.6 K0.4 and qK =A L0.5 K0.5.

(p) Calculate the effect of the wage subsidy of consumer surplus and producer surplus.

(q) Calculate the government’s expenditure on wage subsidies for workers in the meat-processing industry.

(r) What is the welfare effect of the wage subsidy?

1.3 Wage subsidies & the market for butchers

In the previous part of the question, we assumed that the government gives a $1 per unit of labour input subsidy to firms for employing low-skilled workers, and that the after-subsidy effective wage rate for butchers is $4 faced by meat-processing firms.

(s) Derive the labour demand curve of both KK and MM (the cost-minimising quantity of labour as a function of wages) under the assumption that the production functions are qK =A L0.5 K0.5 (with A equal to the value you found in question e) and qM = L0.6 K0.4 , the rental rate of capital r=$10, the market equilibrium prices and quantities are equal to what you found for questions (f) and (i).

(t) Verify that the labour demand curves are downward sloping. Calculate the wage elasticity of labour demand for KK and MM if w=$5. Comment on the difference in elasticity, and why these might be different.

(u) Calculate the market labour demand curve, assuming that there are 10 domestic and 5 foreign-owned firms in the market. Calculate the market-level wage elasticity of labour demand if w=$5.

(v) Study the effect of the wage subsidy on the market wage rate for butchers if (i) labour supply is perfectly inelastic, (ii) labour supply is perfectly elastic and (iii) labour supply is upward-sloping. Which of these was our (implicit) assumption in part 1.2? Use graphs to illustrate your answer.

Exercise 2: Oligopoly

Now assume that the meat-processing industry is a duopoly, with two firms: MM’s-grinders and KK’s cutters. Their production functions are as described before: qM = L0.6 K0.4 ; qK = L0.5 K0.5 ;the wage rate is $5 and the rental rate of capital is $10. The market demand for processed meat is: Q=225 – 9p

2.1 Collusion

Imagine that the two firms ‘collude’, they form a cartel.

(a) What will be the market price, the market output, the output of each firm and the cartel’s total profits? Explain.

2.2 Cournot equilibrium

Now the two firms do not collude, they compete on quantities à la Cournot.

(b) What are the two firms’ best response functions? Show you calculations.

2.3 Comparison: Perfect Competition vs. Collusion vs. Cournot

(d) Calculate the Consumer Surplus, the Producer Surplus, and total Welfare for the collusive (cartel) and the Cournot equilibrium. Compare with the situation of perfect competition. Comment.

2.4 Bertrand Competition with identical products

Assume initially that the two firms compete on prices à la Bertrand. Also suppose that the production functions and factor prices are as before: qM = L0.6 K0.4 ; qK = L0.5 K0.5 ;the wage rate is $5 and the rental rate of capital is $10.

(e) Is there a Bertrand equilibrium price? What would this be? Would both firms stay in the market? Explain briefly.

2.4 Bertrand Competition with differentiated products

Now the two firms compete on prices à la Bertrand, and they also have the same (constant) marginal (and average) costs MCK = MCM = ACK = ACM =10.

The two firms initially sell identical products, and the market demand for processed meat is: Q=225 – 9p

(f) What is the Bertrand equilibrium price and the market equilibrium quantity?

(g) What are the two firms’ output and profit? Assume for simplicity that if if KK’s and MM’s prices are equal, consumers ‘flip a coin’ to decide which to buy.

Now MM successfully lobbies in parliament to obtain the “True Hungarian” product label1, thereby differentiating its products from KK’s. As a result the demand functions facing the two firms now are:

QM=145 – 6pM + 9pK and QK=100 – 9pK + 6pM

(h) What are the Bertrand equilibrium prices and the quantities?

(i) Was it worth it for MM to obtain the “True Hungarian” product label (compare with the undifferentiated products case)? How much is the maximum amount that MM is willing ‘contribute’ to the ruling party’s re-election campaign (in order to ensure that they can keep the label)?

(j) Are KK hurt by MM obtaining the “True Hungarian” label? Why or why not?

The meat-processing industry in Hungary is perfectly competitive, and there are two types of firms operating, domestic and foreign. Two…

The meat-processing industry in Hungary is perfectly competitive, and there are two types of firms operating, domestic and foreign. Two representative (typical) firms are the domestic-owned Marton’s Meat-grinders and the foreign-owned Kostas’ Kutters (henceforth MM and KK), which use slightly different technology, their production functions are:

For MM: qM = L0.6 K0.4

For KK: qK = L0.5 K0.5
Currently, the wage rate is $5 and the rental rate of capital is $10.
(a) Write down the cost-minimization condition for the two firms.

For MM: Min K, L wL0.6 + rK0.4 + λ[q- f(L,K)]

For KK: Min K, L wL0.5 + rK0.5 + λ[q- f(L,K)]

(b) What are the equations for the (long-run) expansion paths? Comment.

MPL0.6/MPK0.4 = w/r

MPL0.5/MPK0.5 = w/r

i) Average Cost

AC =

AC For MM: = = 15/(3*4) = 1.25

AC For KK: = = 15/(2.5*5) = 1.2

ii) Marginal Cost

MC =

MC For MM: = = 5/(3*4) = 0.42

MC For KK: = = 5/(2.5*5) = 0.4
(d) Are foreign-owned firms (like KK) able to survive in a competitive market?

NO
(e) Assume that KK is more efficient than MM, such that: qK =A L0.5 K0.5. A is a scaling factor, representing managerial quality (say Kostas organises production more efficiently and is better at disciplining workers). What is the value of A if both types of firms are able to stay in the market?

= 0.42/0.4

= 1.05
(f) What will be the output price in this market?

= 1.05(5*0.5)(10*0.5)

=1.05(2.5*5)

=1.05*12.5

= 13.13
(g) Assume that the demand function for processed meat is Q=225 – 9p. What is the equilibrium quantity?

13.13 = 225 – 9p

9p = 225 – 13.13

9p = 211.87

P = 211.87 / 9

P = 23.54
(h) Calculate the elasticity of demand at the equilibrium point.

= (23.54 + 13.13) / 2

= 18.34

(i) If there are currently 10 domestic firms (like MM) and 5 foreign firms (like KK) in the market, how much will each of them produce?

qM= 10(5*0.6)(10*0.4)

= 120

qK= 5(5*0.5)(10*0.5)

= 62.5

(j) Calculate the capital and labor input for the two types of firms if qM = L0.6 K0.4 and qK =A L0.5 K0.5 (assume that A is equal to what you found in question e).

120 = 1.05(2.5LK)

62.5 = 2.4LK

……………………………..

Capital and labor input for MM =

120 = 2.63LK

= 120 / 2.63

= 45.63

Capital and labor input for KK

62.5 = 2.4LK

= 62.5 / 2.4

= 26.04

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