Answer to Question #165402 in Macroeconomics for retaa

Question

Part III: 20%

Question One: The following production table provides estimates of the maximum amounts of output possible with different combinations of two input factors, X and Y. (Assume that these are just illustrative points on a spectrum of continuous input combinations.)

a)     Do the two inputs exhibit the characteristics of constant, increasing, or decreasing marginal rates of technical substitution? How do you know?

b)     Assuming that output sells for $3 per unit, complete the following tables:

 

c) Assume that the quantity of X is fixed at 2 units. If output sells for $3 and the cost of Y is $120 per day, how many units of Y will be employed?

d) Assume that the company is currently producing 162 units of output per day using 1 unit of X and 3 units of Y. The daily cost per unit of X is $120 and that of Y is also $120. Would you recommend a change in the present input combination? Why or why not?

Question two: The total cost equation of a firm is given by the equation where TC is total cost and Q is the level of output.

 

a. What is the firm’s total fixed cost?

b. What is the equation for the firm’s total variable cost (TVC)?

c. What is the equation for the firm’s average total cost (ATC)?

d. What is the equation for the firm’s marginal cost (MC)?

Answer 1

$$Solution$$

Let's consider the table below,

a)The inputs exhibit the characteristic of a decreasing marginal rate of technical substitution throughout. For the decreasing MRTS, the slope of the production (isoquants diminishes as one input is increasingly substituted for another. This can also be achieved algebraically by holding $x$ or $y$ constant in the in input-output matrix and noting the decline in the relative marginal product of the other input as its usage level grows.

b) If an output goes for $3, then our table will look like the one below

c)$y=3$ will be taken. The marginal value of the first three units of $y$ is greater than their marginal cost. The marginal value of the fourth unit is only $114 or 6 when fixed at 2 units, less than it's cost, and hence the firm would empty no more than 3 units of $y$ .

d) A change would be in order because the firm could produce 188, units at the same cost using 2 units of each output, that is, the marginal product to price ratios of the two inputs are not equal at the current input proportions relatively less $y$ and more $x$, is needed to provide an optimal combination.

Question 2

Assuming that the $TC=4000+5Q+10Q^2\\$ then,

a) Total Fixed cost is, $TFC=4000$

b) $Total\ Variable\ cost=\frac{TFC}{Q}=\frac{4000}{Q}\\$

c) $Average\ total\ cost=\frac{TVC}{Q}=50+10Q$

d$Marginal\ cost=\frac {\delta\ TC}{\delta q}=5+20Q$