Suppose the utility function over two goods X and Y is given by U(X, Y ) = X + 3Y . Suppose the consumer's income is $40 and wants to spend it all on these two goods. Px=$2 per unit and Py=$4 per unit. 1) Write down the equation of the budget line. Draw it on a graph, labeling the intercepts. Graph consumption of X on the horizontal axis, and consumption of Y on the vertical axis. ( 5 marks) 2) What is the slope of this budget line? ( 5 marks) 3) What is the optimal bundle that maximizes utility and show it on a graph. ( 5 marks) 4) At the optimal bundle, how is the marginal rate of substitution compared to the rate at which the consumer can substitute one good for another along the budget line? (5 marks)