Question

Answer all questions
1. Explain the “Law of Equi-marginal utility” as applied in consumer theory
2. Compare the equilibrium of a firm under perfect competition and monopoly
3. Suppose that the total cost function of a firm operating in the short run is given by
TC = Q2+ 24Q+6 Where TC=Total Cost Q= Quantities produced
Required: i) The ATC function ii) The marginal cost function iii) The average variable cost function iv) Calculate the average fixed cost where Q= 8
4. Distinguish between income and substitution effects of a price change for a consumer
5. Discuss the history of development of Economics as a discipline
{Total =30 Marks}

Answer 1

1. The law of diminishing marginal utility states that the marginal utility derived from the consumption of each additional unit of a good keeps on diminishing. This implies that the marginal unit derived from the last unit of the good is the least. The 'Law of Equi-marginal utility' is related to this law of diminishing marginal utility. According to the consumer theory, the law states that the total utility of a consumer is maximized when he or she allocates his or her income in such a way that the satisfaction derived from the last penny (or rupee) spent on each good remains the same.
For example, let us assume that the consumer spends his money income on two goods X and Y which cost as prices P_X and P_Y respectively. The consumer has to allocate the income between these two goods X and Y. If he purchases more quantity of X, then according to the law of diminishing marginal utility, the MU_X (marginal utility of X) will keep on diminishing. Similarly, for good Y, MU_Y will decline. The consumer will be able to maximize his utility only when the last unit of money spent on good X equal the last unit of money spent on good Y. Hence, the income allocation should be in such a way that the marginal utilities derived from both goods X and Y are equalized, and can be expressed mathematically as:

3. The Total cost function of the firm is provided in the problem as:
TC = Q² + 24Q + 6, where TC is the Total cost and Q is the Quantities produced.

i) ATC or Average Total Cost is the cost incurred by the firm for per unit of output. It is calculated by dividing the Total cost of a firm by Quantities produced.

When TC = Q² + 24Q + 6, AC is

ii) The marginal cost is the net increase or decrease in the total cost by producing an additional unit of output. It is the net change in cost per unit change in the quantity of output. In the problem, the total cost is provided as: TC = Q² + 24Q + 6

The Total cost of first unit of output is TC (1) = (1)² + 24 (1) + 6 = 31
The Total cost of second unit of output is TC (2) = (2)² + 24 (2) + 6 = 58.
The marginal cost in this case is calculated as: TC (2) - TC (1) = 58 - 31 = 27.

iii) The total cost function includes fixed as well as variable costs. The total variable cost is the cost which changes with per unit of output and the fixed cost is the cost which does not change with per unit of output. In the problem, the total cost function is: TC = Q² + 24Q + 6 and the total variable cost in this function is the part TVC = Q² + 24Q.
Average variable cost is the per unit variable cost and is obtained by dividing total variable cost by quantity produced, that is,

In the problem, TVC =  Q² + 24Q, and

iv) The fixed cost is the non-variable part of the cost function. It does not change with the change in any unit of output. In the problem, the total cost function is: TC = Q² + 24Q + 6. The part of the function which is non-dependent on quantity is 6. This part of the cost will remain fixed even if there is no quantity produced at all and even if there is large production. Thus, even if the quantity produced is Q=8, the fixed cost will remain 6.