Question

1. The table below shows Louisa’s preferences for the number of books she buys per month, holding the prices of all goods constant.

Income (thousands of $)	Optimal number of books	Income elasticity of demand for books
10	3
20	5
30	10
40	15
50	15

1. Complete the income elasticity of demand column for the table above (using the midpoint method). Are books ever an inferior good for Louisa? At what level(s) of income are books a luxury?
2. Draw a smooth approximation of Louisa’s Engel curve for books.

Answer 1

optimal numba I of Income (thousands of demand Income elasticity i for books books 10 xx xx 10:75 10 O 1.67 idos; ensino sul 50 15. e ly you , arral 1.. 400g N 15 - Now for the income range of $10-$20 pocentage change in income (m) = (20-10] #100 = 66.67 (20+ 10) and demanded for broksi(Qd) pucentage Change in quantity = 45713*10 = 50 demand = income elasticity of procentage Change in Qid pucentage clage in m - now SE 0.75 Scanned with CamScanner

for the income range of $20-$30 (m) i ind pucentage change in income 130-20) *100 = 40 130720) 2 Quantity demanded for books (ad) .. and pucentage change in 110-5)_ *10= 66.67 pots) Now, Income elasticity of demand Cem) - pucentage change in Qd . pucentage change in m 66.67 = 1.67 - Ho 054-OR fondo Edoti 191-00 dispone unge stik 75 war - Corja ) i posts aspen Lisbny Scanned with CamScanne - -

for the income range of $30-$40% pucentage change in income (h) - 10 28.57 = 40-30) 140+30) 2 for books (ad): and pucentage change in quantity demanded - (15-10) *100 = 40 115 +10) - Pucentage clouge in Qd 2 Now Income elasticity of demand? pucentage change in m - _40 : 14 L 28.57 $ 40-$50! for the income range of Prentage change in income (m) :- 150-40) 4100 = 22:22 (30440) prcentage change in Quantity demanded for books (ad), AS-15) *100 = 0 115H5] 2 Now change in Qd income elasticity of demand? = prcentage pucentage clarge in rete m - 22:22 Scanned with CamScanner

As value of in come elasticity of demand is positive at all price ranges, hence books are neun an inferior good to Louisa. Now for luxury goods we know that value of income elasticity of demand is greater than I always from the table we can see that at income levce of $30 + and $40 value of income elasticity of demand is greaty than a. Honce books are one goods at in come leves of $30 and $40 by Now we can draw Louisa's Engel cmue for books blacing in come (m) on the antical anis and quantity a books are on the horizontal ani's

"Income (thousands of Engel cmue for books . 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 is optimal » bu books CS Scanned with CamScanner