Suppose there are two goods, co ee (C) and tea (T). The consump- tion set is R2 +, so both goods can be consumed in arbitrary non-negative quantities. Abdul owns
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Suppose there are two goods, co ee (C) and tea (T). The consump-
tion set is R2
+, so both goods can be consumed in arbitrary non-negative
quantities.
Abdul owns 2000 grams of co ee but does not own any tea. He has
no other wealth. The price of co ee is pC = 2 (in Dhs per gram) and
the price of tea is pT > 0 (in Dhs per gram). Abdul can sell co ee to
earn income, which he can then use to buy tea or co ee. He can also
throw co ee away (at no cost).
Abdul's preferences can be represented by the utility function
u(c; t) = -(800 - c)2 - (800 - t)2;
where c is the quantity of co ee (in grams) and t is the quantity of tea
(in grams).
(a) In separate diagrams, illustrate (i) the map of Abdul's indi erence
curves, (ii) Abdul's constraint set.
(b) How much co ee and tea does Abdul decide to consume when (i)
pT = 2, (ii) pT = 3, and (iii) pT = 4?
(c) Illustrate Abdul's demand for co ee as a function of the price of tea (pT > 0) in an appropriate diagram.
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- Mylie’s total utility from singing the same song over andover is 50 utils after one repetition, 90 utils after tworepetitions, 70 utils after three repetitions, 20 utils afterfour repetitions, 250 utils after five repetitions, and 2200utils after six repetitions. Write down her marginal utilityfor each repetition. Once Mylie’s total utility beginsto decrease, does each additional singing of the songhurt more than the previous one or less than the previousone?Carol needs to decide how to spend her wealth on sh and chicken.For Carol, 1 lb of sh is equivalent to 2 lb of chicken. Her preferencecan be represented by the utility functionu(x; y) = 2x + ywhere x is the quantity of sh (in lbs) and y is the quantity of chicken(in lbs). The consumption set is R2+. (a) Draw two typical indi erence curves for Carol, one correspondingto a utility level of u1 and one corresponding to a utility level u2,where 0 < u1 < u2. Make sure you label the slope of the indif-ference curves and the intercepts with the horizontal and verticalaxes.(b) Suppose the price of sh is $1:5 per lb and and the price of chickenis $1 per lb. Carol has $20 to spend on sh and chicken.(i) Draw Carol's budget set, labeling the slope and the interceptpoints clearly.(ii) How much sh and chicken will Carol choose to purchase? I am looking for an answer to the points (c) and (d) below (c) Suppose now that the price of sh increases to $2 per pound.(i) Draw Carol's budget set,…A child is given $4.80 of pocket money to be spent on either hard candies or chocolates. Chocolates cost 40 cents and hard candies $1.20 each. The marginal utilities derived from each product are as shown in the following table. Number of Items MU of Chocolates MU of Hard Candies 1 2 3 4 5 6 7 8 60 50 40 30 20 10 5 150 140 120 100 80 70 50 20 Which combination would give the child the maximum utility out of spending $4.80? 6 chocolates and 2 hard candies 8 chocolates and 0 hard candies 3 chocolates and 3 hard candies 0 chocolates and 4 hard candies
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