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Question 1: Households A households utility over consumption C and leisure l is U - U(C,0) Cl 1. Plot the households indifference curve for U-80 for values of C andlless than 20 (i.e. find the curve containing all combinations of C and ( such that U(C, 0) 80) The household has a time endowment of h=16 hours per day. The wage rate per hour is w 1.25. The households labour income is therefore wNs, where N-h-l-16- l is the time spent working every day. Since this household does not have any other sources of income, its consumption will be C=wNs_n(h-C ) 1.25(16-1) 2. How much leisure can this household enjoy at most if it does not buy any consumption goods? How much can it consume at most if it uses all its time endowment to work? 3. Draw the households budget line in the same figure as the indifference curve. 4. What is the households optimal consumption bundle (i.e. how many units of C and ( will it choose to consume)? Now lets solve the same problem analytically. Remember that the households budget constraint can be written C1.25(16-0) 5. Substitute the budget constraint into the utility function to obtain an expression for 6. 7. 8. utility that depends on C only Maximize this utility to obtain the optimal amount of L. (Take the derivative of this expression with respect to l, set the derivative equal to zero, solve for L.) Find the optimal amount of C by plugging your result for ( into the budget constraint How does the optimal consumption bundle you just derived compare to the one you found graphically before?

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Answer #1

(1) The indifference curve represents various combination of C and l. The following table shows the various combinations of C and l.

Plot the above values as shown below to obtain the indifference curve:

It is the straight line in black.This indifference curve shows the combinations of C and l for U(C,l)=80

(3)

The budget line is shown in the above plot in part(1). It is the straight line in orange colour with coordinates (0,20) and (16,0).

The household's optimal consumption bundle is (C,l) = (10,8).

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