Consider the following production function: Q = (1-x-1)yk. Assume we are dealing with the short run, so capital is fixed, i.e. k=1. Assume the prices of both inputs x and y are 1 and the cost of capital is r = 3. Assume that the price of the output is 3. Suppose the size of the market is limited and only 4 units can be sold at most. Answer the following: (A) Is this business viable? Use math to justify your answer. (B) Give an example of a business that can be represented by this function. Justify why you think this function appropriately models it. Hints: Look at other problems you solved. Find the break-even point. Find where minimized costs equals total revenue. You will need costs and revenue as a function of Q. Use the break even to assess whether this business is a good option. Think about what x could mean.
Consider the following production function: Q = (1-x-1)yk. Assume we are dealing with the short run, so capital is fixed, i.e. k=1. Assume the prices of both inputs x and y are 1 and the cost of capital is r = 3. Assume that the price of the output is 3. Suppose the size of the market is limited and only 4 units can be sold at most. Answer the following:
(A) Is this business viable? Use math to justify your answer.
(B) Give an example of a business that can be represented by this function. Justify why you think this function appropriately models it.
Hints: Look at other problems you solved. Find the break-even point. Find where minimized costs equals total revenue. You will need costs and revenue as a function of Q. Use the break even to assess whether this business is a good option. Think about what x could mean.
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