If both planned savings and planned investment increase by $1 billion at each real interest rate, explain the change in the real interest rate and equilibrium quantity of loanable funds.

Changes in interest rates in various segments of the financial market affect the willingness of economic participants to borrow, invest, save or consume and, accordingly, translate into the dynamics of monetary indicators, consumer and investment demand. All other things being equal, the lower the interest rates, the higher the growth in lending, consumption, and investment, and vice versa.

Within the framework of the transmission mechanism of monetary policy, several channels of the influence of interest rates on lending and savings activity are distinguished. First, the current level of interest rates directly affects the attractiveness of loans and deposits for bank customers and, accordingly, the choice between current and future consumption (the last stage of the interest rate channel of the transmission mechanism). Lower rates make it easier to finance running costs with borrowed funds and less attractive to save by postponing spending for the future. On the contrary, when rates rise, the attractiveness of deposits increases, and the attractiveness of lending decreases. This channel, associated with the demand for financial products from bank customers, is called the interest rate transmission channel.

Second, changes in interest rates affect the market value of stocks, bonds, real estate, and other assets: when rates go down, asset prices rise, and when they go up, they decrease. At the same time, prices react most strongly and quickly in the financial asset market, where transactions are completed faster than, for example, in the real estate market. Since the assets owned by companies and the population can serve as collateral for loans, the increase in their value increases the ability of companies and households to attract borrowed funds. This additionally contributes to the expansion of lending when the key rate decreases or reduces lending activity when the rate rises (balance sheet transmission mechanism, or asset price channel).

Third, the change in the market value of assets caused by changes in interest rates affects not only the clients of banks but also the banks themselves. The growth in the value of bank assets is a source of profit for banks, increasing bank capital, thanks to which banks can increase the volume of lending operations. At the same time, the decline in the value of banking assets caused by the rise in interest rates reduces the capital of banks and limits the ability of banks to increase lending. However, for some large banks, the equity capital adequacy factor can affect the volume and structure of lending operations.

Fourth, the current level of rates in the economy influences the choice of banks between more and less risky operations (risk-taking channel). The decline in market rates limits the interest income of banks, and this stimulates banks to issue more loans, including by expanding lending to riskier (and, therefore, lending at a higher rate) borrowers.

Fifth, the functioning of the credit channel, as well as the risk-taking channel, is associated with the influence of interest rates on the debt burden on bank borrowers (the level of the debt burden shows what part of borrowers' income goes to interest payments and debt repayment). The increase in the debt burden, on the one hand, reduces the ability of borrowers to service their current liabilities and, accordingly, to attract new loans, reducing demand in the credit market. On the other hand, the growing debt burden on the borrower (and, consequently, the increased risk that the loan will not be repaid in full or in violation of the established terms) leads to the formation of additional reserves by banks for possible losses, which reduces bank capital and limits the ability of banks increase lending (credit channel). In addition, interest rates are used in standard risk analysis models. If the rates (and debt burden) on the borrower decrease, the bank evaluates the borrower as more reliable and is more willing to provide loans to such borrower (risk-taking channel).

In addition to the impact through lending activity, the growing debt burden also directly affects the aggregate demand in the economy, since the more funds borrowers spend on servicing their obligations, the less money remains.