Question

9 kmlv.github.io Question 2: A consumer has an income of $1,000 to spend on food and medicine. The price of one unit of food is $5 and the price of one unit of medicine is $10. For each question, write down the mathematical expression of the budget constraint and draw it carefully. Put food on the x-axis and medicine on the y-axis. Label the incercepts,slopes, and kinks. 1. Suppose the consumer receives coupons for 50 units of food and those can only be used to buy food 2. Suppose the consumer receives coupons for 50 units of food and can sell the coupons at half of the market price of the food. 3. Instead of the coupon, the consumer receivesa 20% discount for additional units of food that exceed 100 units. That is, the consumer pays $5 for each of the first 100 units and $4 for each additional unit.

Answer 1

M = 1000, P_F = 5, P_M = 10, B middot C rightarrow mp_m + fp_f = M coupons for 50 units of F, (not transferable) if F lessthanorequalto 50, p_F = 0 mp_m = M 10m = 1000 if F > 50, 10m + 5f = 1000 max possible food constant 50 + 1000/5 = 250 Now coupons can be sold max income from selling coupons = 50 times 5/2 = 125 New income M' = 1000 + 125 = 1125 Now B middot C 10m + 5f = 1125 max m = 112.5, max f = 225 Now f > 100, p_f' = 5 - 20 % of 5 = 4 so f lessthanorequalto 100, B middot C implies 10m + 5f = 1000 f > 100, income left implies 1000 - 100 times 5 = 1000 - 500 = 500 New B middot C: rightarrow 10m + 4f = 500 max possible f = 100 + 500/4 125 = 225