# Production functions and cost

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Each day Paul, who is in third grade, eats lunch at school. He likes only Twinkies (T) and Orange Slice (S), and these provide him a utility of

Utility = U (T, S) =

Every day his mother gives him $1 to spend on lunch. Assume that it is possible to purchase fractional amounts of both the goods.

a. If Twinkies cost $0.10 each and Slice costs $0.25 per cup, what is his budget constraint? Write down the budget equation and draw the budget line.

b. Where does the budget line intersect (touch) the indifference curve for U = ?

c. Show different combinations of T and S that satisfy the budget constraint, give the corresponding utility value, and verify that the combination of T and S obtained in part b, in fact, maximizes Paul's utility.

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Solutions:1

<br><br>a) If Twinkies cost $0.10 each and Slice costs $0.25 per cup, what is his budget constraint? Write down the budget equation and draw the budget line:

<br><br> Budget constraint $0.10T + $0.25S = $1

<br><br> to draw the budget line: for example consider this two points A( T=0; S=4) and B(T=10; S=0) AND c(T=5, s=2)

<br><br>

<br><br>B) Where does the budget line intersect (touch) the indifference curve for U =10^1/2. To answer a question like this first, one should determine the TMS between T and S which is the point in which budget line is tangeant to the utility fonction. U't/U's=Price of T / price of S. (1/2*S^1/2*T^-1/2)/(1/2*T^1/2*S^-1/2) = $0.1/$0.25 After doing all the claculation we get S/T=0.1/0.25 which is S=0.4*T . we will now replace S in ...

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