Will an increase in interest rate (which leads cost of borrowing, thus leading increased cost of production) cause aggregate supply to shift?

Yes, it Would. Build a macroeconomic model, to understand how the “average price of all goods and services produced in an economy affects the total quantity of output and the total amount of spending on goods and services in that economy.”

Aggregate Supply is the total of all final goods and services which companies expect/plan to produce in a given time period. It also can be viewed as the total amount of goods and services that manufacturers or traders are willing to sell at a given price in an economy.

There are two schools of thought for a Long Run Aggregate Supply: One is the Monetarist “Reganomics” view and two the Keynesian view—Government investing/spending—in the economy. The curve behaves upward sloping in the short run and vertical, or close to vertical, in the long run.

The behavior of the model curve is affected by several factors:

Figure 1 credit: "Building a Model of Aggregate Demand and Aggregate Supply" by OpenStaxCollege, CC BY 4.0 and Khan Academy

1. Adverse supply shocks shift Aggregate Supply (AS) to the left. Usually, a rapid increase in oil prices can cause a supply shock. Unexpected rise in taxes or inflation can also shift AS to the left. A vertical long-run shift of the AS curve suits better the effect of natural disasters or setbacks in the economy by a corrupt or incompetent governments.

2. Changes in the short run resource prices can alter the Short Run Aggregate Supply curve. Unless the price changes reflect differences in long-term supply, the Long Run Aggregate Supply is not affected.

3. Economic expectations of Inflation. If suppliers expect to sell goods at rapidly growing prices in the future, they will be less willing to sell in the current period. As a result, the Short Run Aggregate Supply will shift to the left. New investment and better technology can result in productivity improvements as well as competent political administration, although some factors can only affect Aggregate Supply in the short run.

4. A rightward or an increase in AS implies an increase in productive capacity or technology change in the economy. One can think of this as an outward shift in the production possibility curve. An increase in the quality and/or quantity of the factors of production and/or technological improvements or any other reason for an increase in productivity can cause an outward shift of the Aggregate Supply curve.

Governments can influence (AS) through Supply Side policies such as improvements in health and education services not an increase in the money supply which tends to inflation. An rise in natural resources like new discoveries of energy sources or a shift to cheaper resources can also shift the AS curve to the right.

Aggregate Demand (AD) and Formula

The accepted economic model Aggregate Demand is the total of Consumption, Investment, Government Spending and Net Exports (Exports – Imports).

Aggregate Demand = C + I + G + (X – M). It shows the relationship between Gross National Product (GNP) and the Price Level. C= investment, I= spending, G= government spending X= spending on exports, minus M=spending on imports.

1. When domestic prices increase, then demand for imports increases (since exports are inversely related to imports. (X-M)

2. When inflation increases, real spending decreases as the value of money decreases. This shifts Aggregate Demand to the left.

3. Real Interest is the minimal interest rate adjusted to the inflation rate. When inflation increases, nominal interest rates increase to maintain real interest rates. Lower real interest rates will lower the costs of major products and will increase business capital spending.

4. If consumers expect price inflation in the future, they will tend to buy now causing aggregate demand to increase or shift to the right affecting a shift in GDP as well as aggregate demand is the amount of total spending on domestic goods and services in an economy.

The downward-sloping aggregate demand curve shows the relationship between the price level for outputs and the quantity of total spending in the economy as prices come down demand increases.

Aggregate demand measures must include all four components :( C + I + G + (X – M)

Consumption

Investment

Government spending

Net exports= (exports minus imports)

The aggregate demand model curve:

Figure 2 credit: "Building a Model of Aggregate Demand and Aggregate Supply" by OpenStaxCollege, CC BY 4.0 and Khan Academy

The interest rate effect is that as economic output increases, the same purchases will require more money or credit to accomplish. This additional demand for money and credit will push interest rates even higher. But higher interest rates will reduce the amount of borrowing by businesses for investment and also reduce borrowing needs by households to buy homes and/or cars and added together, it reduces both consumption and investment spending.