There are 2 firms in the yoghurt market dannon and yoplait

Question

Question: There are 2 firms in the yoghurt market, Dannon and Yoplait. They produce yoghurt using milk (M) and capital (K) according to the production function

q = 2(√MK)

where q is the quantity of yoghurt produced. The price of milk is p_m = 4, and the price of capital is de noted r. The price of yoghurt is denoted p_y.

In the short run, both firms have a fixed plant size, so that capital is fixed. Dannon has plant size K¯D = 100, while Yoplait has plant size Y = 81

A. Which firm has the highest market share? Comment in light of the capital endowments.

B. Compute the quantity of milk used by each firm in equilibrium. Derive the marginal product of milk in each firm at the equilibrium. Comment.

C. If r = 0.25, are the firms making a profit?

Suppose that the price of milk increases to pm = 4.50.

D. Qualitatively, what happens to the supply curves of Dannon and Yoplait? To the market supply curve?

E. Qualitatively, what happens to the equilibrium price of yoghurt? the equilibrium quantity Q^e? Explain.