Indifference curves and budget lines — practice questions

(a) Budget equation: £100 = 5X + 10Y

X-intercept: 100/5 = 20 units of X Y-intercept: 100/10 = 10 units of Y Slope: −5/10 = −0.5 (1 X costs 0.5 Y)

(b) Check bundle (8, 6): 5(8) + 10(6) = 40 + 60 = £100 ✓ — on the budget line.

MRS at optimum = P_x/P_y = 5/10 = 0.5

The consumer is willing to trade 0.5 units of Y for 1 unit of X (at the margin), which equals the market price ratio.

(a) Initial Budget Line: Let C be the quantity of coffees and S be the quantity of sandwiches. The budget equation is: Income = (Price of Coffee × C) + (Price of Sandwich × S) $60 =$3C + $6S$

Initial Price Ratio (Slope): Price Ratio = P_c / P_s = $3 /$6 = 0.5 The slope of the budget line is -0.5. This means the student must give up 0.5 sandwiches to get 1 more coffee.

(b) After Price Change: The price of sandwiches (P_s) falls from $6 to$5. The new budget line is: $60 =$3C + $5S$

Verify New Optimal Bundle: The student consumes 10 coffees and 6 sandwiches. Total spending = ($3 \times 10) + ($5 × 6) = $30 +$30 = $60.$ This bundle is affordable and lies on the new budget line.

New Price Ratio and MRS: At the new equilibrium, the MRS must equal the new price ratio. New Price Ratio = P_c / P_s = $3 /$5 = 0.6 Therefore, at the new optimal point, the MRS = 0.6. This means the student is now willing to give up 0.6 sandwiches for one extra coffee, reflecting the fact that coffee is now relatively more expensive than before (or sandwiches are relatively cheaper).