2. Suppose there are n identical consumers, each with a utility function u(x, y) = ax...

 

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2. Suppose there are n identical consumers, each with a utility function u(x, y) = ax = x+y. Each consumer has different disposable income w. The price of good x is p dollars, and the price of composite good y is equal to 1 dollar. Assume a > 0 and b> 0. (Hint: Question 1) (a) Calculate the marginal utility of good x and good y. Then, calculate the marginal rate of substitution between good x and good y. (b) Calculate the individual demand of consumer 1 for good x. (c) Calculate the aggregate demand for good x. (d) Draw a graph showing the market demand curve for good x. (e) Discuss whether an increase in disposable income for each consumer lead to an increase in the consumption of good x? This increase in disposable income can result from various factors, such as a decrease in taxes, government stipends, or other forms of income support. (f) Discuss the effect on demand for good x if there is an increase in the price of good x. This increase in the price of good x can result from various factors, such as production cost increases, supply shortages, increased demand for inputs, tax increases for the good, or regulatory changes. 2. Suppose there are n identical consumers, each with a utility function u(x, y) = ax = x+y. Each consumer has different disposable income w. The price of good x is p dollars, and the price of composite good y is equal to 1 dollar. Assume a > 0 and b> 0. (Hint: Question 1) (a) Calculate the marginal utility of good x and good y. Then, calculate the marginal rate of substitution between good x and good y. (b) Calculate the individual demand of consumer 1 for good x. (c) Calculate the aggregate demand for good x. (d) Draw a graph showing the market demand curve for good x. (e) Discuss whether an increase in disposable income for each consumer lead to an increase in the consumption of good x? This increase in disposable income can result from various factors, such as a decrease in taxes, government stipends, or other forms of income support. (f) Discuss the effect on demand for good x if there is an increase in the price of good x. This increase in the price of good x can result from various factors, such as production cost increases, supply shortages, increased demand for inputs, tax increases for the good, or regulatory changes.