Question: Smith's utility function is U(x1, x2) = x1 + ln x2 x1 - stampsx2 - beer Smith's budget: p1 x1 + p2 x2 = m

Smith's utility function is U(x1, x2) = x1 + ln x2

x1 - stampsx2 - beer

Smith's budget: p1 x1 + p2 x2 = m

p1 - price of stamps p2 - price of beer m - Smith's budget

a) What is Smith's demand for beer and stamps?

b) Is it true that Smith would spend every Taka in additional income on stamps?

c) What happens to demand when Smith's income changes (i.e. find the income elasticity)?

d) What happens to demand when p1 and p2 increase (i.e. find the price elasticities)?

[Hint: For a) Given prices, p1 and p2, find the quantities x1 and x2 which maximise Smith's utility! Necessary condition: MRS= MU1/MU2; Find MRS; Optimum occurs when x2= p1/p2, Using x2, Find x1 from the given budget line

For (b), compare x1 and m;For (c) and (d), use the formula of income elasticity (em1, em2) and price elasticity (ep1, ep2]; for each, put the value of x1 found on problem (a)]

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