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(solution) ECON 204 MICROECONOMICS - HOMEWORK 1 Date due: February 17, 2016,


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ECON 204 MICROECONOMICS - HOMEWORK 1

 

Date due: February 17, 2016, in class.

 

1. (5 points) If prices are p1 = 5 and p2 = 3, give an example of a commodity bundle which you cannot afford with income m = 300TLs. What is the cost of your example

 

bundle?

 

2. (10 points) Calculate the subsidy rate ? (?sigma?) on good 1 such that the example bundle you gave in question 1 becomes just affordable (the price you pay for good 1

 

thus becomes (1 ? ?) p1 and the commodity bundle then lies on your budget line).

 

3. (10 points) The government imposes a value added tax on good 1, at the rate ? percent. Your dad tells you that he will transfer you an income exactly equal to the amount of

 

tax you pay to the government. Are you worse off or better off or indifferent

 

(compared with the situation before the tax)? Explain?a figure will surely help.

 

4. (35 points) The government offers Ali a food stamp for 75 TLs, with which he can buy 200 TLs food. If he buys it, Ali cannot sell the food stamp to others. Denote the price

 

of food by pF. Call the second good, ?expenditures on all other goods? which therefore

 

is priced p2 = 1.

 

(i)

 

What quantity of food does this stamp buy (as a function of pF)? Since Ali pays 75

 

TLs to buy this quantity, what is the effective food price for him (as a function of

 

pF)? Therefore, how much this stamp is subsidizing Ali per unit of food he buys?

 

(ii)

 

Put food on the horizontal axis, good 2 on the vertical axis and draw a budget line

 

for Ali, with m = 1000. Indicate the values of the intercepts of the budget line with

 

each axis (the intercept could be a number or may depend on pF.)

 

(iii)

 

Draw Ali?s budget line when he buys the food stamp. On your figure, indicate

 

clearly the new budget set of Ali (the set of bundles he can consume).

 

(iv)

 

Answer the same question (draw budget line and set), assuming that Ali can sell

 

the entire food stamp to somebody else.

 

(v)

 

Answer the same question (draw budget line and set), assuming that Ali buys the

 

food stamp and gives it for free to his friend in need of food.

 

5. (10 points) Whatever bundle of the two goods I have, giving up 2 slices of dark bread to get 5 slices of white bread leaves me indifferent. Draw my indifference curve.

 

6. (10 points) I always consume 5 spoons of cereal with 4 spoons of milk. More of any of the two goods outside the 4-to-5 proportion does not change my satisfaction. Draw my

 

indifference curve.

 

7. (10 points) The equation of an indifference curve is U = u(x1, x2) where U is fixed satisfaction (utility) level. Differentiate this utility function with respect to x1 and x2

 

holding the utility level constant (dU = 0) and obtain the expression of the marginal

 

rate of substitution between the two goods.

 

8. (10 points) Draw indifference curves for preferences that are rational (complete, reflexive, transitive) and convex, but not monotonic.

 


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