Question

a. A firm uses only two inputs: capital (K) and labor (L).Currently, the firm’s choice of capital (K) and labor (L) are such that marginal product of capital is 80 and the marginal product of labor is 10. If one put Labor on the x-axis, derive the slope of the firm’s isoquant given the information above (include the formula you use to do this).

b. The price of capital (Pk) is $40 and the price of labor (PL) is $20. Given this information, derive the slope isthe slope of the isocost(include the formula you use to derive this).

c. Graph the firm’s isocost when total cost is 200$, labeling endpoints.

d. Given the prices and productivities above, show (explain) if the firm could reduce its cost while keeping output constant (or, instead, show, if it could produce more output for the same cost). That is,should the firm want to use more of one input and less of the other? Prove including showing if it would change its input mix, whether it wants to use more capital or labor .Hint: use your answers in a. and b.

Please answer all the parts, will give thumb down if its not all parts

Answer 1

1) Given, marginal product of capital = 80

Marginal product of labour = 10

Slope of Isoquant = marginal rate of technical substitution.

Marginal rate of technical substitution denotes how much of the capital is been replaced by amount of labour. It shows a sacrificing ratio and it is negatively sloped.

=-10/80 = - 0.125

2) Next question is about how to find the slope of isocost line. The formula to find the slope of isocost line is to find the relative price of inputs.

Slope of isocost line = 20/40

= 0.5

3)

4) In order to change the cost we can change the use of output in the production process then there will be a shift in the isocost line which shows that there will be a change in the total cost.