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
(c) What is the average and the marginal cost for the two firms?
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
gera
econ_hw_v1.docx
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