Rashida has a monthly income of $200.which sheallocates between two goods meat and potatoes,
(a)suppose meat cost$4 per pound and potatoes cost $2 per pound.drawv her budget constraint.
(b)suppose that her utility function is given by the equation u(M,P)=2M+P. WHAT COMBINATION OF MEAT AND POTATOES SHOULD SHE BUY TO MAXIMIZE HERU TILITY?(MEAT AND POTATOES ARE PERFECT SUBSTITUTE.)
To solve this problem, we need to understand Rashida's budget constraint and then determine the combination of meat and potatoes that will maximize her utility.
(a) Budget Constraint:
Rashida's monthly income is $200. She can allocate this income between meat (M) and potatoes (P). The price of meat is $4 per pound, and the price of potatoes is $2 per pound.
To draw her budget constraint, we need to consider the quantity of each good she can purchase with her income. Let's assume she buys x pounds of meat and y pounds of potatoes.
The equation representing Rashida's budget constraint is:
4x + 2y = 200
This equation shows that the total amount spent on meat (4x) plus the total amount spent on potatoes (2y) should equal her monthly income of $200.
Now, let's draw her budget constraint graphically. To do so, we need to rearrange the equation to solve for y:
2y = 200 - 4x
y = (200 - 4x) / 2
y = 100 - 2x
Now we can plot the graph by assigning x and y values and drawing a line based on the equation y = 100 - 2x.
(b) Maximizing Utility:
Rashida's utility function is given as u(M, P) = 2M + P. It indicates that she values meat and potatoes equally, as they are perfect substitutes for her.
To maximize her utility, we need to choose a combination of meat and potatoes that lies on the budget constraint line and satisfies her utility function.
You can compute the utility level by substituting the values of M and P into the utility function equation. To maximize her utility, you need to find the combination of M and P that yields the highest possible value of u(M, P).
On the graph, you will need to identify the point on the budget constraint line where the highest value of u(M, P) is achieved. This point will correspond to the combination of meat and potatoes that Rashida should buy to maximize her utility.
Note that the slope of the budget constraint line is negative (-2). This means that as Rashida consumes more meat, she needs to decrease her consumption of potatoes to stay within her budget.
By examining the graph and calculating the utility function at different points on the budget constraint line, you will be able to identify the combination of meat and potatoes that maximizes her utility.