. On a monthly basis, the consumer has an income of N$5000 that he spends on food and clothes.gf The prevailing Consider a rational consumer, whose consumption bundle is composed of two goods, food and clothes prices of food and clothes are N$100 per unit and N$200 per unit, respectively. Suppose the following function represents the utility that a consumer gets from consuming different units of food and clothes:

U=2x_1^2 x_2^3

Where U represents the total utility, x is the unit of food per month and is the unit of clothes per month. Based on this information answer the questions below:

i.Determine the units of food and clothes in the consumer's optimal consumption bundle.(8)

Suppose the price of food increased to N200 per unit ceteris paribus (i.e. income and price of clothes remained constant). Estimate the impact of this price change on the utility of the consumer. (2