A consumer's consumption-utility function for a two period horizon is 0.5 U(cg.G) =c,G" ne consumer's earned income stream is given by mo, mi and the market rate of interest is r. a) Write the intertemporal budget constraint in present value terms. If the consumer does not consume anything in peripd 0, what is the most she can consume in period 1? b) Draw a graph that shows optimal consumption in each period co* and c1*. What is the slope of her budget line? c) Solve the problem for optimal consumption in each period Co* and c¡*.
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- Rajiv is buying pizza and salad for a company lunch. Suppose that a slice of pizza costs $2.00, and a bowl of salad costs $4.00. Let E be the amount in dollars that Rajiv spends on pizza and salad. If Rajiv buys P slices of pizza and S bowls of salad, then the total amount of money he spends (E) can be represented by the equation Now rearrange the equation you wrote above so that S is written in terms of E and P. The quantity of salad he buys can be represented by the equation Suppose Rajiv has $32.00 to spend on pizza and salad; that is, E = $32.00. Complete the following table with the values of P or S that make the equation true. Hint: To complete the first row, determine the number of salad bowls Rajiv can purchase with $32.00, when the number of pizza slices he purchases is 0. Budget Pizza Salad (Dollars) (Slices) (Bowls) 32.00 32.00 8 32.00 Use the black line (plus symbols) to plot the line illustrating the combinations of pizza and salad that Rajiv can purchase with a budget of…Tim is buying pizza and salad for a company lunch. Suppose that a slice of pizza costs $4.00, and a bowl of salad costs $5.00. Let ♬ be the amount in dollars that Tim spends on pizza and salad. If Tim buys P slices of pizza and S bowls of salad, then the total amount of money he spends (B) can be represented by the equation Now rearrange the equation you wrote above so that S is written in terms of E and P. The quantity of salad he buys can be represented by the equation Suppose Tim has $40.00 to spend on pizza and salad; that is, E = $40.00. Complete the following table with the values of P or S that make the equation true. Hint: To complete the first row, determine the number of salad bowls Tim can purchase with $40.00, when the number of pizza slices he purchases is 0. Budget Pizza (Dollars) (Slices) 40.00 0 40.00 5 40.00 Use the black line (plus symbols) to plot the line illustrating the combinations of pizza and salad that Tim can purchase with a budget of $40.00. SALAD (Bowis) 14…Use the black line (plus symbols) to plot the line illustrating the combinations of salad and pizza that Andrew can purchase with a budget of $30.00. PIZZA (Slices) 14 12 10 00 4 2 O to 0 2 4 8 8 SALAD (Bowls) 10 12 14 Initial Budget New Budget ? Now suppose Andrew's income is cut in half: That is, he has 50% less money to spend than he did before. On the previous graph, use the blue line (circle symbols) to plot Andrew's new budget constraint. Which of the following statements best summarizes the pattern of causality captured by the graph above? Check all that apply. The relationship between S and P is not a causal relationship. A change in E causes a shift of the budget constraint. A change in S causes a change in P. A change in P causes a change in S.
- On a given evening, J. P. enjoys the consumption of cigars (c) and brandy (b) according tothe functionU(c, b) = 20c− c²+ 18b − 3b²a. How many cigars and glasses of brandy does he consume during an evening? (Cost isno object to J. P.)b. Lately, however, J. P. has been advised by his doctors that he should limit the sum ofglasses of brandy and cigars consumed to 5. How many glasses of brandy and cigarswill he consume under these circumstances?Exercise 2 (The Saving Schedule). Consider a two-period economy populated by identical households with preferences defined over consumption in period 1, C1, and consumption in period 2, C,, and described by the utility function Assume that households are endowed with Y, kilos of apples in period 1 and with Y, kilos of apples in period 2. Let P, and P, denote the price of apples in periods 1 and 2. Households can save (or borrow) at the nominal interest rate i. Let r denote the real interest rate, so that the gross real interest rate is 1 +r = P, P, (1 + i). Let St denote saving in kilos of apples. 1. State the household's budget constraints in periods 1 and 2. 2. Derive the household's intertemporal budget constraint in terms of C1, C2, Y1, Y,, and r. 3. State the household's utility maximization problem. 4. Find the optimal level of consumption in period 1, C,, in period 2, C2, and the associated level of saving, S,. Express your answer in terms of Y,, Y,, and r. 5. Now assume that…Kenji is buying salad and pizza for a company lunch. Suppose that a bowl of salad costs $3.00, and a slice of pizza costs $4.00. Let E be the amount in dollars that Kenji spends on salad and pizza. If Kenji buys S bowls of salad and P slices of pizza, then the total amount of money he spends (E) can be represented by the equation Now rearrange the equation you wrote above so that P is written in terms of E and S. The quantity of pizza he buys can be represented by the equation Suppose Kenji has $48.00 to spend on salad and pizza; that is, E= $48.00. Complete the following table with the values of S or P that make the equation true. Hint: To complete the first row, determine the number of pizza slices Kenji can purchase with $48.00, when the number of salad bowls he purchases is 0. Pizza Budget Salad (Dollars) (Bowls) (Slices) 48.00 0 48.00 48.00 8 0
- The vending machine in Katherine's office building offers cans of pop and candies. Katherine's utility function is U = 3PC, where P is the amount of pop consumed per %3D week and C is the amount of candy consumed per week. Pop costs $1 and candy costs $0.5 per bag. If Katherine has $10 to spend, she will consume A bags of candy.Suppose that there are T periods to maximize over. Show that the intertemporal budget constraint is Ct+2 Yt+2 Yt+1 (1+r) (1+r)² (1 + r)² Ct + Ct+1 (1 + r) + 2+...+ Ct+T+1 (1+r)² \ T = Yt + + +...+ Yt+T+1 (1+r)1. An individual derives utility from the consumption of a basket of goods, c and leisure time, given by U(c, l) =cºl(1-a) where 0 < a < 1, is a constant; and must decide how to allocate her time between work, L and leisure to maximize her utility. The individual has a total of 24 hrs in a day (L + l = 24) and total consumption is constrained by her income; i.e., c = wL, where w the real per hour, is taken as given. (a) Solve for the optimal labor supply.
- Suppose a consumer has a monthly income of m = 100 which she spendson two commodities: french fries (x1) and beef jerky (x2). The price offrench fries is p1 = 2 and the price of beef jerky is p2 = 5.(a) Write down the consumer’s budget constraint (equation).(b) What is the maximal consumption of french fries (this is calledthe real income in french fries).(c) Find the maximal consumption of beef jerky (real income interms of beef jerky).Consider the 2-period household model that you have seen in class. Suppose the household wants to consume equal amounts in both periods. She earns $100 in the first period and $150 in the second period. The interest rate depends on whether she saves or borrows. The interest rate on saving is 1%, while the interest rate on borrowing is 10%. What is her optimal consumption? Note: Type in your answer approximated to two decimal points, i.e., your answer must be of the form "999.99". I will not be able to fix correct answers that were entered incorrectly, such as "999.999" or "999,99" or "999". In case the last digit in the correct answer is zero, e.g., "999.90" or "999.00", Blackboard will automatically delete it and you should not do anything about it.The expression, M = PXX+ PYY is called a budget constraint where M = amount of money available for expenditure; PX= price of commodity X; PY= price of commodity Y; PXX= expenditure on commodity X; PYY= expenditure on commodity Y. Use M = PXX+PYY to express Y as a function of X and note that the graph of this function is called a budget line. Algebraically derive: (1) the y-intercept; (2) the x-intercept. State what determines the slope of the budget line. Graph the function for M = 120; PX= 3; PY= 5 andshow what happens to the original budget line if M decreases by 25% with PX, PY constant.