Question

You live right on the border between Massachusetts and New Hampshire. In New Hampshire, wine costs $10 per bottle. In Massachusetts, wine also costs $10 per bottle, but Massachusetts adds a tax of $5 per bottle. No matter where you buy wine from, you like 5 parts food for every 1 part wine, implying that your utility function is U=min(F,5W). Food costs $1 per unit in both New Hampshire and Massachusetts and is not taxed in either state. You have $90 per week to spend on food and wine.

(a)  What's the equation for the budget constraint in New Hampshire

(b)  If you buy all of your wine in New Hampshire, how much wine and food will you buy

(c)  Make a graph showing your budget constraint, utility maximizing bundle, and your utility maximizing indifference curve

(d)  What is the equation for the budget constraint in Massachusetts

(e)  At first, you buy all of your wine in Massachusetts until you find in store you like in NH. Then you buy all of your wine in NH because it's cheaper. Given your utility function, will this price change generate both an income and a substitution effect? Explain

(f)   Eventually, you decide to buy some of your wine in Massachusetts and some in NH. The wine store in Massachusetts is closer to your home than the store in NH so you usually buy your first 2 bottles of wine in Massachusetts but drive to NH for any bottle of wine after the first. Graph this budget constraint for food and wine.

Answer 1

Price of Quiche is $5 and Price of Wine is $10 upto 5 units.

based on this information we can plot a budget line ab

When a consumer.. Buys all quiche, than the total units that can be brought with given budget constraint are 20 units (100/5 = 20), this is plotted on y-axis.

when She wishes to consume only wine, total units she can be brought are 100/10= 10 units

We can plot this on the x-axis.

If we join these points a and b, we get a budget line, where a consumer can buy with various combinations.

Now , if the price of wine decreases from 6th unit onwards, (these are the promotional offers gven to motivate sales and increase their revenues)

Consumer brought 5 units of wine at $50, remaining $50 if spent on purchasing only wine than she can buy 10 units, so a total of 15 units can be brought by $100. With this promotional offer. Now the new budget line will be 'a c d'. Due to this offer Cindy will buy more of wine and less units of quiche. We can see this at two indiferrence levels I and II.

For getting 50% discount on extra units, a consumer will buy more than 5 bottels.

If this offer dosent exist, or if the price of wine was reduced to half an all units, than the cosnumer will buy based on his utility,consumption may be lower than 5 units.