# Sarah's utility function for housing (H) and other consumable goods (C) is U = H^4 C^6 a. Show...

## Question:

Sarah's utility function for housing (H) and other consumable goods (C) is U = H^4 C^6

a. Show mathematically that her marginal utility from each good is diminishing.

b. If her monthly income is $3000, housing costs$2 per square foot to rent, and other consumable cost \$10 per unit, how much H and C will she purchase each month? Show that you can get the same answer, using the shortcut (budget share) method, and using the Langrarian method.

c. Find her marginal rate of substitution as a function of H and C (let good 1 be H, and good 2 be C). What is the value of MRS at the solution point you found in part b? What does it mean, in words?

d. Find Sarah's marginal utility of income (solve for lambda).

## Utility Maximization:

The utility function represents the level of enjoyment that could be obtained from consuming different goods. The utility is maximized when the per dollar marginal utility of all goods are equal.

Sarah's utility function for housing (H) and other consumable goods (C) is U = H^4 C^6

a.

• {eq}MU_H=dU/DH=4H^3C^6 \\ dMu_H/dH=12H^2C^6 {/eq}
• {eq}MU...

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