Question

1.A firm's demand function for a certain good is given by. Its total cost function is . What output level maximizes the firm's profit?

 

2.An individual’s utility function is given by

where is the amount of leisure measured in hours per week and is income earned measured in cedis per week.

 

Determine the value of the marginal utilities, when = 138 and = 500. Hence estimate the change in utility if the individual works for an extra hour, which increases earned income by GH¢15 per week. Does the law of diminishing utility hold for this function?

 

3.A firm’s total cost function is given by

Where  and  denote the number of items of goods 1and 2, respectively that are produced. Using the substitution method, find the values of  and  which minimize costs if the firm is committed to producing 40 goods of either type in total.

Answer 1

1. The output level at which MR = MC maximizes the firm's profit.
2. Marginal utility is the added satisfaction a consumer gets from having one more unit of a good or service. The law of diminishing marginal utility states that all else equal as consumption increases the marginal utility derived from each additional unit declines.
3. To minimize total costs TC the firm should produce such quantity Q for which TC'(Q) = MC = 0.