Question

Please explain this, especially Part A in detail (how to draw).

Someone posted the answer of this but do not understand it.

Firm "Challenger Inc". uses two inputs (input K1 & input K2) to produce its final good (Q). Specifically, it needs two (2) units of input K1 and one (1) unit of input K2 to produce one unit of its final good. The production function as this function by the Managerial Director of Challenger Inc.: Q = F( K1, K2 ) = Min( 0.5K1 , K2 )

A- Draw Isoquant curves of this production function (K2 on the vertical axis and K1 on the horizontal axis).

B- The firm is currently producing 10 units of the final good (Q). If the price of both inputs (K1 and K2) is equal to 10, what is the minimum total expenditure the firm needs to incur to produce the 10 units of Q output?

C-Now suppose Challenger Inc. has a budget of $ 450 and the prices of inputs K1 and K2 have not changed. What is the maximum number of units of the final good the firm can produce?

D- If the firm’s budget was $459, would your answer in part c change? (Note: You can only produce integer units of Q output).

E- Refer to Part C. If Challenger Inc.'s budget was $468, would your answer in part c change? (Note: You can only produce integer units of Q output).

Answer 1

The given production function is:

a. The production function can be broken down as follows:

The production function's kinks will lie along the line .

Plotting the isoquants for production levels 2,3,4, and 5.

with on the horizontal axis and on the vertical axis.

b. At equilibrium, the firm will employ half a unit of and one unit of to produce one unit of output. Hence, at equilibrium:

Since quantity produced is 10 units, quantity of the two inputs is:

The firm's cost function is given by:

Substituting the above computed values in the cost function:

c. The firm's objective is:

The cost minimization quantities of the two inputs will also maximize production in this case, as shown in the diagram below:

Substituting the following values into the firm's cost function we get the maximum quantity that can be produced:

d. The firm's objective is:

Plotting the objective with the constraint:

Since only integral quantities of the final output can be produced, production will remain at 15 units and the quantities of both inputs will also remain the same as the previous part. The extra $9 will be unused.