U(x,y)=3x+y, where x and y represent the quantities of two goods, X and Y. The ocnsumer has I=60 , to spend on the two goods, and good Y costs Py=2 per unit. The price of good x, Px is also exogenous.
1. with good x on the horizontal axis and good Y on the vertical axis, draw indifference curve for utility levee U=6. Show the exact coordinates of at least two points on the curve. On the same diagram similarly draw the indifference curves for the utility levels U=18 and U=30.
2 Draw consumer's budget line and calculate the first order condition for this problem. On your budget line, show optimal point. Justify your answer.
3. If optimal point = 10 dollar, calculate the consumer's demand function which shows Qd as a function of its price.
4. Graph demand function that you found in part 3, showing the specific coordinates of the points with Px=2, 4, 6, 8, 10.
5. Calculate the consumer's elasticity of demand for X, at the point Px=4 and Px=8.