Suppose That a Consumer Has Utility U(X,Y) = 2XY

question 7

Essay

Suppose that a consumer has utility U(X,Y) = 2XY + X and income of $499 to spend on goods X and Y.
a. The prices of X and Y are $1 and $2 per unit, respectively. Use a Lagrangian to solve for the optimal basket of goods.
b. Suppose that the price of X increases to $2 per unit. Use a Lagrangian to solve for the new optimal basket of goods. Find the total effect of the price change on the consumption of each good.
c. Use a Lagrangian to find the substitution effect of the increase in the price of good X on the consumption of each good. What income would the consumer need to attain the original level of utility if the price of X increased to $2 per unit?
d. Find the income effect of the increase in the price of good X on the consumption of each good. Are the goods normal or inferior? Explain.
e. Show that the total effect of the increase in the price of X is equal to the sum of the substitution effect and the income effect.

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Definitions:

Effective Message

Communication that is clearly understood, received as intended, and accomplishes its intended purpose.

Vital Signs

Measurements of the body’s most basic functions, including temperature, pulse, respiration rate, and blood pressure.

Normal Limits

The range of values considered standard or acceptable for physiological measurements or laboratory test outcomes.

Pedal Pulse

The palpable beat of the artery at the top of the foot, used to assess blood circulation to the lower limb.