1.) l need to first build a graph to these specifications: Draw a budget constraint with vertical intercept (0,8) and horizontal intercept (4,0). Zach's indifference curves are downward sloping straight lines with a slope of -1 i.e. they all have vertical intercept (0,N) and horizontal intercept (N,0) for some number N. Draw Zach's indifference curves.Label the bundle(s) that Zach will consume when optimizing.

2.) Now suppose the price of the "x-good" falls to become 4 times smaller than it was originally. Draw Zach's new budget constraint. Draw in Zach's indifference curves and label the new optimal bundle(s).Interpret Zach's indifference curves: are the good substitutes or complements to Zach?

3.)Emily likes pretzels and Pepsi. She bought 12 bottles of Pepsi for $3 each. Her marginal utility for the twelfth bottle was 9 utils. She also bought 5bags of pretzels for $4 per bag. Her marginal utility for the fifth bag was 8 utils. Assume Emily exhausted her budget on this purchase of Pepsi and pretzels, but wanted to maximize her utility. Would she have been better off buying more Pepsi and fewer pretzels, more pretzels and less Pepsi, or was her purchase already optimal? Assuming her marginal utilitiesare constant across all levels of consumption. Arepretzels and Pepsi complements or substitutes to Emily?