Question

A manufacturing company that produces tires has the following production function and marginal product function

The machine that molds the tires costs $100. Each unit of raw rubber cost the firm $3. The firm sales each tire at a price of $50. The production process produces a waste that is dumped into a nearby river which kills fish. Because of the smaller fish population, this financially harms local fishermen. More specifically, for every unit of raw rubber the tire manufactory uses it reduces the profits of local fishermen by two dollars.

1. Solve for the profit maximizing level of . Does it correspond to the optimal value on your graph in problem a? [2 Point]
2. What is the profit when is used? [1 Point]
3. Solve for the socially optimal level of production . Does it correspond to the socially optimal production level on the graph you constructed in part d? [1 Point]
4. How do the net social benefits differ between the profit maximizing level of production and the socially optimal level of production . (Hint: Net social benefits are given by ) [1 Point]
5. How large should the tax be to incentivize the tire manufacture to produce at the socially optimal level ? [1 Point]

Answer 1

Ans - PRODUCTION FUNCTION - Production function shows the relationship between quantities of productive factor and the amount of product obtained .

Production function formula = Q = F(K,l)

Q = Quantity produced

K = Capital

L = Labour

Marginal product function = A marginal product function may be defined as additional output produced in the existing output .

MC = The change in cost/change in quantity.

A - Firms decide how many inputs to produce in order to produce :

K for Capital

L for Labour  

So , firm produce output

Y = F(K,L)

This function is called the production function .

Profit maximize where revenue is more than cost .