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.

Comprehend the developmental stages and substages proposed by Jean Piaget, including an understanding of behaviors indicative of each substage.

Identify the age ranges associated with each of Piaget's stages of cognitive development.

Recognize the central aspects and accomplishments of different stages of cognitive development according to Piaget.

Understand concepts related to thought processes in children, such as egocentrism, conservation, and symbolic functioning.

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Definitions:

Customer Needs

The wants and requirements that customers expect to be fulfilled by a product or service.