Question

Problem 1 (2.5 marks). Suppose there are only two time periods, today (period 1) and tomorrow (period 2), and only one consumption good, let's call it food. Assume that food is a perfectly divisible good. Let ci and c2 denote the amount of food consumed today and tomorrow, respectively. Note that here we use subscripts to denote time periods. The price of food today is equal to Pi = P, but as the rate of inflation is > 0, the price of food tomorrow is P2 = (1 + 7)P. Denise has wealth wi today and w2 tomorrow. Furthermore, as food is perishable, Denise cannot buy today and save for tomorrow, but wealth can be saved or borrowed. If Denise saves some of her wealth in period 1, she earns interest on her savings at a rate of rı > 0 per period. On the other hand, if Denise decides to borrow, she has to pay an interest rate of r2 > 0 per period. Let's assume this is a realistic assumption, otherwise private banks would not exist that 1 >r2 > 11. (a) Draw Denise's budget set in a (C1,C2)-plane, i.e., with C1 in the horizontal axis and c2 in the vertical axis, and mark the bundle that Denise consumes if she neither borrows nor saves. (b) Indicate carefully the intercepts of the budget line(s) with both axes. Hint: to find the intercept with the horizontal axis, you need to consider what is the largest amount of food Denise can consume today, if she spends all of her wealth (today's and tomorrow's) in food today. (c) Determine the slope(s) of the budget line.

Answer 1

Consumer lives for a period = Today and tomorrow (1) Consumption = ca and (z Prices today = PI =P Prices Tomorrow - Pz = (i+1)p Juhenest rate on saving - ri Junerest rate on borrowing = V2 1 82 > r o Denise budget set Picit P2 (z ² witWz ie. Total expenditure Total Income Pat (147) P C2 = witwa. (a) Cal (1+r) W1 + WzT Point E where (HAP PLITA) and C2 = We PCI+) where Denise neither borrows nor saves (2= W2 P(ITA) IC G = W wypta) Citra)

b) PCit(+7) P C2 = Wit wz Horizontal intercept, Where (2=0 » when Denise consume all his wealth today - Pei= Wit Wz (1+r2) Cita) Total expenditure - Total wealth in terms of on consoming present discounted food today value a= Wit was a litra) Vertical in P(1+A) C₂ = (1+r) wit We C2 = (1+r) W) + Wz P(+7) P(Ita) 1 She saves her wealth in porod 1, and receive (i+Y) W period a slope of budget line = In C)