Question #58505

Table below gives Usman’s marginal utility schedule for commodity X and commodity Y. Suppose that X and Y are the only commodities available, the price of X and the price of Y are $1, and Usman’s income is $8 per time period and is all spent. (a) Indicate how Usman should spend his income in order to maximize his total utility. (b) What is the total amount of utility received by Usman when he is at his optimal point? (c) State mathematically the equilibrium condition for the consumer. [Hint: Equi-Marginal Utility]

Expert's answer

X and Y are the only commodities available, the price of X and the price of Y are Px = $1 and Py = $1, and Usman’s income is I = $8.

(a) Usman should spend his income in such way, that MUx/Px = MUy/Py and Px*Qx + Py*Qy = I, if he want to maximize his total utility. So, we have a system of 2 equations: MUx/1 = MUy/1 and 1*Qx + 1*Qy = 8, so MUx = MUy and Qx + Qy = 8.

(b) The total amount of utility received by Usman at his optimal point will be the sum of total utilities, that correspond to the marginal utilities from the previous question.

(c) The equilibrium condition for the consumer is MUx/Px = MUy/Py and Px*Qx + Py*Qy = I.

(a) Usman should spend his income in such way, that MUx/Px = MUy/Py and Px*Qx + Py*Qy = I, if he want to maximize his total utility. So, we have a system of 2 equations: MUx/1 = MUy/1 and 1*Qx + 1*Qy = 8, so MUx = MUy and Qx + Qy = 8.

(b) The total amount of utility received by Usman at his optimal point will be the sum of total utilities, that correspond to the marginal utilities from the previous question.

(c) The equilibrium condition for the consumer is MUx/Px = MUy/Py and Px*Qx + Py*Qy = I.

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