The optimal consumption bundle is where O A. cay-t-s. OB. the consumer chooses the consumption bundle that minimizes minimal total utility OC. MRS -1=r. OD. the marginal rate of substitution in the current period equals the marginal rate of subetitution in the future period. O E. Cs.
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- For this question, assume that indifference curves are strictly convex, consumption andleisure are normal goods, and the optimal amounts of consumption, leisure, and labor arealways positive. A wage increase ______. (SE = substitution effect; IE = income effect)(a) increases labor supply via the SE and decreases labor supply via the IE(b) decreases labor supply via the SE and decreases labor supply via the IE(c) increases labor supply via the SE and increases labor supply via the IE(d) decreases labor supply via the SE and increases labor supply via the IE(e) Can’t tell without knowing the utility functionMary spends all her budget on statistical software (S) and office supplies(O). Her preferences can be represented by the utility function: U(S, O) =2 ln(S) + 3 ln(O). Compute the marginal rate of substitution of software for office supplies. Is the MRS increasing or decreasing in S? How do we interpretthis?Terry’s utility function over leisure (L) and other goods (Y) is U (L, Y) = Y + LY. The associated marginal utilities are MUY = 1 + L and MUL = Y. He purchases other goods at a price of $1, out of the income he earns from working. Show that, no matter what Terry’s wage rate, the optimal number of hours of leisure that he consumes is always the same. (a) What is the number of hours he would like to have for leisure? (b) Determine the MRS of leisure for labour (c) Draw a leisure-influenced labor curve
- Terry’s utility function over leisure (L) and other goods (Y ) is U(L, Y ) = Y + LY. The associated marginal utilities are MUY = 1 + L and MUL = Y. He purchases other goods at a price of $1, out of the income he earns from working. Show that, no matter what Terry’s wage rate, the optimal number of hours of leisure that he consumes is always the same. (a) What is the number of hours he would like to have for leisure? Determine the MRS of leisure for labour (b) Draw a leisure-influenced labor curveThe Marginal Rate of substitution depends on the O a. Tastes and preferences of the consumer B Price level of goods income of the consume Oc.income of the consumer O d. Availability of goodsHenry's utility function is u(x,y)=max{x+3y,3x+y}. (a) Suppose Henry's current consumption bundle is (2,1.5), what is his current utility level? If he consumes the bundle (1.5,2), will his utility change from the current utility level?
- Consumption when young and consumption whenold are both normal goods for Seymour, a workersaving for retirement. When the interest rate falls,what happens to Seymour’s consumption when old?a. It definitely increases.b. It definitely decreases.c. It increases only if the substitution effect exceedsthe income effect.d. It decreases only if the substitution effectexceeds the income effect.(d) What point in the graph will lead to utility maximizing with the budget line LZ and the indifference curves as shown above? Please label the point C. (e) What is the marginal rate of substitution (slope of the indifference curve) at the utility maximizing point you have shown in (d)?(f) Please explain why the consumer will not choose point A or point B.Consider an individual who receives utility from consumption, c, and leisure, l. The individual has L time to allocate to work, n, and leisure. The individual’s consumption is a function of how much he works. In particular, c = root n. The individual’s maximization problem is max U =ln(c)+θl subject to c = √n n+l=L where θ > 0. Solve the maximization problem. Hint: Substitute both constraints into the objective function.
- Question 1 Consider a person with the utility function U (C, L) = (1 − α) log C + α log L, where L is leisure time and C is consumption of other goods measured in dollars. The person has V dollars of non-labor income and a wage of w. There are T hours available for either working or leisure. 1. Write down the person’s budget constraint. Draw a graph representing this constraint, taking care to label the axes and key points. 2. What are the person’s marginal utilities for consumption and leisure? What is her marginal rate of substitution between leisure and consumption in terms of C, L, and α? 3. Write down a condition involving the person’s marginal rate of substitution that characterizes her optimal choice. Represent this condition graphically and interpret in words. 4. Solve for the person’s optimal choices of leisure and consumption, L ∗ and C ∗ , in terms of T, V , w, and α. 5. How does L ∗ change as you increase wage w and non-labor income V ? 6. How does C ∗ change as you…Mrs. Rochester earns $4500 a week and spends her entire income on computers andpastries, since these are the only two items that provide her utility. Furthermore, a) Draw an indifference curve showing the optimum choice. Label the optimum aspoint A. What would be the marginal rate of substitution at the point thatcorresponds to the optimal consumption choice? Interpret the marginal rate ofsubstitution. b) What would be the new marginal rate of substitution that corresponds to theoptimal consumption choice? Interpret the marginal rate of substitution. c) Assume for this question only that when the price of computers decreases, less ofthat good is demanded. Illustrate the income and substitution effect of this pricedecrease.Mary has two dinner options available: eating a home cooked meal for $150 per meal, or at a restaurant for $260 per meal. Her weekly budget is $2500.iii. What would be the marginal rate of substitution at the point thatcorresponds to the optimal consumption choice? Interpret the marginalrate of substitution. iv. Suppose the price of a home cooked meal increases to $200 and incomeincreases to $4200. Show the impact of the new budget line relative to theoriginal budget line. What would be the new marginal rate of substitutionthat corresponds to the optimal consumption choice? Interpret themarginal rate of substitution.
