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4. Consumer theory (4\%) A plumber likes BEvERages (B) and munchies (M). Their indifference curves for these goods is described by U=f(B,M) =BM0.5, where B=BEvERages in bottles/month and M= bags of munchies per month. The market prices are \$2 per bottle, and \$6 per bag. The plumber has a budget of $48 per month to spend on BEvERages and munchies, and currently buys 12 bottles and 4 bags per month. (a) Are they staying within budget? (b) Graph the plumber's budget line for BEvERages (x-axis) and munchies (y-axis) and plot on their current consumption point. (c) Calculate the plumber's current utility U. (d) Determine their optimum consumption plan for BEvERages and munchies (B,M). (Recall: max U MUx/Px=MUy/Py). (e) The stores don't sell fractional quantities of BEvERages and munchies, only integer counts. Considering this integer constraint, what should the plumber do? (f) How much can the plumber increase their utility by adjusting consumption to this practical optimum? (g) If the government feels that consuming a product has adverse effects on public health and wants to reduce consumption, they may impose a tax. What would the effect of a $0.25 per bottle tax on BEvERages be on the plumber's purchases? Does the tax have the effect the government desires? 4. Consumer theory (4\%) A plumber likes BEvERages (B) and munchies (M). Their indifference curves for these goods is described by U=f(B,M) =BM0.5, where B=BEvERages in bottles/month and M= bags of munchies per month. The market prices are \$2 per bottle, and \$6 per bag. The plumber has a budget of $48 per month to spend on BEvERages and munchies, and currently buys 12 bottles and 4 bags per month. (a) Are they staying within budget? (b) Graph the plumber's budget line for BEvERages (x-axis) and munchies (y-axis) and plot on their current consumption point. (c) Calculate the plumber's current utility U. (d) Determine their optimum consumption plan for BEvERages and munchies (B,M). (Recall: max U MUx/Px=MUy/Py). (e) The stores don't sell fractional quantities of BEvERages and munchies, only integer counts. Considering this integer constraint, what should the plumber do? (f) How much can the plumber increase their utility by adjusting consumption to this practical optimum? (g) If the government feels that consuming a product has adverse effects on public health and wants to reduce consumption, they may impose a tax. What would the effect of a $0.25 per bottle tax on BEvERages be on the plumber's purchases? Does the tax have the effect the government desires