Ag Bm 101 question: Graphing and Prices?
The U.S demand for tomato imports from Mexico: Q=24-P
The supply from Mexico: Q=6+P
$1=10 pesos
When I graph I get that 3 tomatos=$9 Us price, 90 pesos
Then we have to adjust for price when $1=5 pesos. I got $18.
However, if I put the Q given (for example 3) into the supply equation I get an entirely different set of numbers.
Anyone have a clue... a ton of people in my class are totally stumped.
It is not clear whether the price P in your original equations are in pesos or dallars. In any case, I agree that P = 9 when supply equals demand. That corresponds to a quantity of 15, but I have no idea what the units of Q are. It could be thousands of tons per year. 9 pesos (90 cents) is typical of the price per pound these days, seasonally averaged at wholesale level. If a dollar were worth 5 pesos, and the same demand and supply equations applied in pesos, the price in dollars would be double.
To understand the discrepancy you are facing in your calculations, let's break down the problem step by step:
1. Given demand function: Q = 24 - P
The demand function represents the quantity of tomato imports the U.S. is willing to buy at different prices. As the price of tomatoes decreases, the quantity demanded increases.
2. Given supply function: Q = 6 + P
The supply function represents the quantity of tomato imports Mexico is willing to sell at different prices. As the price of tomatoes increases, the quantity supplied also increases.
3. Conversion rate: $1 = 10 pesos
This tells us the exchange rate between U.S. dollars and Mexican pesos. $1 is equivalent to 10 pesos.
4. To find the equilibrium price and quantity, we set the demand equal to the supply function:
24 - P = 6 + P
Rearranging the equation to solve for P:
2P = 18
P = 9
Substituting the value of P back into either the demand or supply function, we can find the equilibrium quantity.
Using the demand function:
Q = 24 - 9 = 15
Using the supply function:
Q = 6 + 9 = 15
Therefore, the equilibrium price is $9 and the equilibrium quantity is 15 tomatoes.
Now, let's address the concern you mentioned about a different set of numbers when substituting a specific quantity (e.g. 3) into the supply equation:
If you substitute a specific quantity (Q) into the supply equation, you will be able to calculate the corresponding price (P) at which Mexico is willing to supply that quantity. However, this does not determine the equilibrium price and quantity. The equilibrium is reached when the quantity demanded by the U.S. matches the quantity supplied by Mexico.
In your example, if you put Q = 3 into the supply equation (Q = 6 + P), you can solve for P:
3 = 6 + P
P = -3
However, this negative price does not make sense in the context of the problem. It indicates that Mexico is not willing to supply 3 tomatoes at any positive price.
To summarize, the equilibrium price and quantity of tomato imports from Mexico to the U.S. is $9 and 15 tomatoes, respectively, according to the given demand and supply functions.