Problem
There are 2 ?rms in the yoghurt market, Dannon and Yoplait. They produce yoghurt using milk(M) and capital (K) according to the production function
q = 2vMK
where q is the quantity of yoghurt produced. The price of milk is pm = 4, and the price of capitalis denoted r. The price of yoghurt is denoted py.In the short run, both ?rms have a ?xed plant size, so that capital is ?xed. Dannon has plantsize KD = 100, while Yoplait has plant size KY = 81.
1. Compute the short-run cost functions of Dannon and Yoplait. (Hint: your short-run costfunctions should depend on r.)
2. Deduce the equations of the short-run supply curves of Dannon and Yoplait. Do the supplycurves depend on the price of capital? the quantity of capital? Comment.
3. Derive the equation of the market short-run supply curve.
The market demand for yoghurt is D(py) = 261 - 40py, where py is the price of yoghurt.
4. Represent the short-run market equilibrium on a graph with price on the vertical axis.
5. Derive the short-run market equilibrium, that is, the equilibrium price pe y, the total equilibrium quantity Qe and the quantities supplied by each ?rm qe D and qe Y .
6. Which ?rm has the highest market share? Comment in light of the capital endowments.
7. Compute the quantity of milk used by each ?rm in equilibrium. Derive the marginal productof milk in each ?rm at the equilibrium. Comment. (Hint: Express marginal cost as a functionof the marginal product of milk, as we did in lecture for labor.)
8. If r = 0.25, are the ?rms making a pro?t?
9. Suppose that the price of milk increases to pm = 4.50.
Qualitatively, what happens to the supply curves of Dannon and Yoplait? To the market supplycurve? Qualitatively, what happens to the equilibrium price of yoghurt? the equilibrium quantity Qe?Explain.
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.