please use microeconomics knowledge to answer this question

please use microeconomics knowledge to answer this question. Please clearly draw the graphs. Thanks

Question 1. (20 marks) Firm 1 and Firm 2 use the same type of production function, Q-f(K, L) where Q= quantity of production K= amount of capital input amount of labour input. However, Firm 1 is only 90% as productive as Firm 2 whereas Firm 2 is fully productive. At a particular level of inputs, a) Does the marginal product of labour differ between the firms? Show your work. (5 marks) b) Does the marginal product of capital differ between the firms? Show your work. (5 marks) c) Does the marginal rate of technical substitution differ between the firms? Show your work. (5 marks) d) Assume that the given production function exhibits the decreasing marginal productivity. Draw the isoquant curves for Firm 1 and Firm 2 in the same diagram. You must label the quantity levels for each firm appropriately (5 marks)

Solution

The Production function for Firm 1 and Firm 2 are given as

q1= 0.9 f(L,K)

q2= 0.9 f(L,K)

then we have MPL = dq1/dL=d(f(L,K)*0.9/dL)=0.9(dq2/dL)

Hence Marginal Product of Labour for Firm 1 = 0.9*  Marginal Product of Labour for Firm 2

Answer for Part B

Similarly MPK= dq1/dK=d(f(L,K)*0.9/dK)=0.9(dq2/dK)=0.9 MPK for Firm 2

MPK1=0.9*MPK2

Answer for Part C

MPL/MPK is Marginal Rate of Technical substitution

(MPL/MPK)1=(MPL1/MPK1)=(0.9MPL2/0.9MPK2)=(MPL2/MPK2)=(MPL/MPK)2